局部密度矩阵的相合性是QMA完全的

通过搜索到判定归约寻找量子部分赋值

Finding quantum partial assignments by search-to-decision reductions

针对量子搜索到判定归约问题，提出一种经典多项式时间算法，通过 $\mathsf{QMA}$ 预言机输出近最优量子证据的部分赋值（约化密度矩阵）近似，基于电路到哈密顿量映射和低能密度矩阵验证问题实现。

Proper and improper density matrices and the consistency of the Deutsch model for Local Closed Timelike Curves

We discuss the concept of proper and improper density matrixes and we argue that this issue is of fundamental importance for the understanding of the quantum-mechanical CTC model proposed by Deutsch. We arrive at the conclusion that under a realistic interpretation, the distinction between proper and improper density operators is not a relativistically covariant notion and this fact leads to the conclusion that the D-CTC model is physically inconsistent.

Gibbs态与局域密度矩阵的相容性

Gibbs States and the Consistency of Local Density Matrices

假设我们有一个n量子比特系统，我们被给定一个局部密度矩阵rho_1，.，rho_m，其中每个rho_i描述量子比特的某个子集。我们说rho_1，.，如果存在全局状态sigma（在所有n个量子比特上），其约化的密度矩阵匹配rho_1，.，ρ_m我们证明了如下结果：如果rho_1，...，rho_m与某个状态σ> 0一致，则它们也与形式为σ ' =（1/Z）exp（M_1+. M_m），其中每个M_i是作用于与rho_i相同的量子位的厄米矩阵，并且Z是归一化因子。(This称为吉布斯状态（Gibbs State）。实际上，我们给出了一个更一般的结果，关于一组期望值的一致性<T_1>，...，<T_r>，其中可观测量T_1，.，T_r不需要通勤。这一结果先前已由Jaynes（1957）在最大熵原理的背景下证明过;这里我们提供一个稍微不同的证明，利用配分函数的性质。

Detecting Consistency of Overlapping Quantum Marginals by Separability

The quantum marginal problem asks whether a set of given density matrices are consistent, i.e., whether they can be the reduced density matrices of a global quantum state. Not many non-trivial analytic necessary (or sufficient) conditions are known for the problem in general. We propose a method to detect consistency of overlapping quantum marginals by considering the separability of some derived states. Our method works well for the $k$-symmetric extension problem in general, and for the general overlapping marginal problems in some cases. Our work is, in some sense, the converse to the well-…

Y-Calculus: A Language for Real Matrices Derived from the ZX-Calculus

We introduce a ZX-like diagrammatic language devoted to manipulating real matrices - and rebits -, with its own set of axioms. We prove the necessity of some non trivial axioms of these. We show that some restriction of the language is complete. We exhibit two interpretations to and from the ZX-Calculus, thus showing the consistency between the two languages. Finally, we derive from our work a way to extract the real or imaginary part of a ZX-diagram, and prove that a restriction of our language is complete if the equivalent restriction of the ZX-calculus is complete.

相关约化密度矩阵的投影纯化

Projective purification of correlated reduced density matrices

本文提出一种最小侵入的投影纯化算法，同时恢复N-可表示性、保持收缩一致性并保留守恒量，在费米-哈伯德模型淬火动力学中优于先前方法。

局部认证多体稳态

Local Certification of Many-Body Steady States

该研究提出了一种基于弛豫的方法，用于高效界多体稳态的期望值，适用于多种一维和二维模型。